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ISSN : 1226-0657

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Vol.27 No.1

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Quadratic(ρ1, p2)-functional Equation in Fuzzy Banach Spaces

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2020, v.27 no.1, pp.25-33
https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.25
Paokant, Siriluk
Shin, Dong Yun
Paokant,, S. , & Shin,, D. Y. (2020). Quadratic(ρ1, p2)-functional Equation in Fuzzy Banach Spaces. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 27(1), 25-33, https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.25

Abstract

In this paper, we consider the following quadratic (&#x03C1;<sub>1</sub>, &#x03C1;<sub>2</sub>)-functional equation (0, 1) <TEX>$$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$</TEX>, where &#x03C1;<sub>2</sub> are fixed nonzero real numbers with &#x03C1;<sub>2</sub> &#x2260; 1 and 2&#x03C1;<sub>1</sub> + 2&#x03C1;<sub>2</sub>&#x2260; 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (&#x03C1;<sub>1</sub>, &#x03C1;<sub>2</sub>)-functional equation (0.1) in fuzzy Banach spaces.

keywords
fuzzy Banach space, quadratic (<tex> ${\rho}_1$</tex>, <tex> ${\rho}_2$</tex>)-functional equation, fixed point method, Hyers-Ulam stability

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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